InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Statement -1: If a and b are positive real numbers and `[.]` denotes the greatest integer function , thenA. Statement -1 is true, Statement-2 is true,, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for statement -1.C. Statement-1 is true, Statement-2 is False.D. Statement-1 is False, Statement-2 is true. |
|
Answer» Correct Answer - A For any non-zero real number x, we have ` 0le {x}lt 1` `rArr 0le ({x})/(x) lt (1)/(x) " for all " x gt 0 rArr lim_(xto oo) ({x})/(x)=0` Hence, statement -2 is true. Now, `lim_(xto0^+)(x)/(a) [(b)/(a)]=lim_(xto0 ^+)(x)/(a)((b)/(x)-{(b)/(x)})=lim_(xto0^+) ((b)/(a)-(x)/(a){(b)/(x)})` ` rArr lim_(xto 0^+)(x)/(a) [(b)/(x)]=(b)/(a)-(b)/(a)lim_(xto0^+)(x)/(b) {(b)/(x)}=(b)/(a)-(b)/(a)lim_(xto0^+)({(b)/(x)})/((b)/(x))` ` rArr lim_(xto 0^+)(x)/(a) [(b)/(x)]=(b)/(a)-(b)/(a)lim_(xtooo) ({y})/(y)," where "y=(b)/(x)` ` rArr lim_(xto 0^+)(x)/(a) [(b)/(x)]=(b)/(a)-(b)/(a)xx0=(b)/(a)" "["Using statements -2"]` |
|